73 citations · 304 across the 61 of their papers we have counts for
7 papers · 1 filter
Convergence of the self-avoiding walk on random quadrangulations to SLE on -Liouville quantum gravity
Ewain Gwynne, Jason Miller
We prove that a uniform infinite quadrangulation of the half-plane decorated by a self-avoiding walk (SAW) converges in the scaling limit to the metric gluing of two independent Br…
Metric gluing of Brownian and -Liouville quantum gravity surfaces
Ewain Gwynne, Jason Miller
In a recent series of works, Miller and Sheffield constructed a metric on -Liouville quantum gravity (LQG) under which -LQG surfaces (e.g., the LQG sphere,…
Scaling limit of the uniform infinite half-plane quadrangulation in the Gromov-Hausdorff-Prokhorov-uniform topology
Ewain Gwynne, Jason Miller
We prove that the uniform infinite half-plane quadrangulation (UIHPQ), with either general or simple boundary, equipped with its graph distance, its natural area measure, and the c…
A distance exponent for Liouville quantum gravity
Ewain Gwynne, Nina Holden, Xin Sun
Let and let be the random distribution on which describes a -Liouville quantum gravity (LQG) cone. Also let and let be a whole-pl…
Active spanning trees with bending energy on planar maps and SLE-decorated Liouville quantum gravity for
Ewain Gwynne, Adrien Kassel, Jason Miller +1
We introduce a two-parameter family of probability measures on spanning trees of a planar map. One of the parameters controls the activity of the spanning tree and the other is a m…
Dimension transformation formula for conformal maps into the complement of an SLE curve
Ewain Gwynne, Nina Holden, Jason Miller
We prove a formula relating the Hausdorff dimension of a deterministic Borel subset of and the Hausdorff dimension of its image under a conformal map from the upper hal…
Joint scaling limit of a bipolar-oriented triangulation and its dual in the peanosphere sense
Ewain Gwynne, Nina Holden, Xin Sun
Kenyon, Miller, Sheffield, and Wilson (2015) showed how to encode a random bipolar-oriented planar map by means of a random walk with a certain step size distribution. Using this e…